Chapter 6.7, Problem 345E

For the following exercises, use Stokes’ theorem to evaluate ${\displaystyle {\iint }_s\left(curlF\cdot N\right)dS}$ for the vector fields and surface.

345. Use Stokes’ theorem to evaluate ${\displaystyle {\int }_c\left(\frac{1}{2}{y}^{2}dx+zdy+xdz\right)}$ , where C is the curve of intersection of plane $x+z=1$ and ellipsoid $x^2+2y^2+z^2=1$ , oriented clockwise from the origin.